“…A few of them are thin film deposition [12], bacteria colony growth [13,14], fluid flow in porous media [15], turbulent liquid crystal [16,17], one dimensional polynuclear growth (PNG) [18,19,20,21], slow combustion of a sheet of paper [22,23]. In addition, many problems are equivalent to the KPZ equation, e.g., Burgers equation [24] describes the vorticity free velocity, directed polymer in random media [25,26] and in random potentials (DPRP) [27], sequence alignment of gene or protein [28,29], heat equation of multiplicative noise obtained via the Cole-Hopf transformation of the KPZ equation.…”